Can you help me here?

1. Aug 24, 2007

deah

Establish the ff. properties of δ(y).

(a) δ(y) = δ(-y)
(b) δ(y) = δ'(y)
(c) yδ(y)= 0
(d) δ(ay)= 1/a δ(y)
(e) δ(y²-a²) = [1/(2a)] [δ(y-a)+δ(y+a)]
(g) δ(y) δ(y-a) = f(a) δ(y-a)
(h) yδ'(y) = -δ(y)

thanks..

2. Aug 24, 2007

cristo

Staff Emeritus
You need to show some work for this sort of question and should, in future, post in the homework and coursework questions forum.

What are you denoting by delta? Do you have a definition to work from?

3. Aug 24, 2007

nicktacik

I may be wrong, but according to a) and b) the only possibility is $$\delta (y) = 0$$. (Which is consistent with c-h).

4. Aug 24, 2007

George Jones

Staff Emeritus
No, $\delta$ is the Dirac delta "function" (distribution, actually), and this thread is in the wrong forum. It should be in either Advanced Physics or Calculus & Beyond, depending on the course for which deah received this as an assigned question.

deah, how would you start a demsonstration of any of these properties?

5. Aug 24, 2007

nicktacik

I was not aware that $$\delta (y) = \delta '(y)$$

6. Aug 24, 2007

George Jones

Staff Emeritus
There must be a typo in (b); note also the typo in (g).

7. Aug 24, 2007

ChaoticOrder

First you have to choose a sequence of functions to work with whose limit is the dirac delta. For instance the sequence

y(x,n) = n^2 x + n for -1/n < x < 0
-n^2 x + n for 0 < x < 1/n
0 otherwise

Then delta(x) = lim(y(x,n),n->infinity)

Use this sequence to prove the properties.